A goal programming procedure for fuzzy multiobjective linear fractional programming problem. (English) Zbl 1047.90081

Summary: This paper presents a goal programming (GP) procedure for fuzzy multiobjective linear fractional programming (FMOLFP) problems.
In the proposed approach, which is motivated by R. H. Mohamed [Fuzzy Sets Syst. 89, 215–222 (1997)], GP model for achievement of the highest membership value of each of fuzzy goals defined for the fractional objectives is formulated. In the solution process, the method of variable change on the under- and over- deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. The approach is illustrated by two numerical examples.


90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C29 Multi-objective and goal programming
90C32 Fractional programming
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[1] Bitran, G.R.; Novaes, A.G., Linear programming with a fractional objective function, Oper. res., 21, 22-29, (1973) · Zbl 0259.90046
[2] A. Charnes, W.W. Cooper, Management Models of Industrial Applications of Linear Programme (Appendix B), vol.-I, Wiley, New York, 1961. · Zbl 0107.37004
[3] Charnes, A.; Cooper, W.W., Programming with linear fractional functions, Naval res. logist. quart., 9, 181-186, (1962) · Zbl 0127.36901
[4] Craven, B.D., Fractional programming, (1988), Heldermann Verlag Berlin · Zbl 0649.90098
[5] Dutta, D.; Rao, J.R.; Tiwari, R.N., Effect of tolerance in fuzzy linear fractional programming, Fuzzy sets and systems, 55, 133-142, (1993) · Zbl 0791.90069
[6] Dutta, D.; Tiwari, R.N.; Rao, J.R., Multiple objective linear fractional programming—a fuzzy set theoretic approach, Fuzzy sets and systems, 52, 39-45, (1992) · Zbl 0786.90088
[7] Dutta, D.; Tiwari, R.N.; Rao, J.R., Fuzzy approaches for multiple criteria linear fractional optimizationa comment, Fuzzy sets and systems, 54, 347-349, (1993)
[8] Dyson, R.G., Maximin programming, fuzzy linear programming and multicriteria decision making, J. oper. res. soc., 31, 263-267, (1980) · Zbl 0436.90106
[9] Hannan, E.L., Linear programming with multiple fuzzy goals, Fuzzy sets and systems, 6, 235-248, (1981) · Zbl 0465.90080
[10] Hannan, E.L., On fuzzy goal programming, Decision sci., 12, 522-531, (1981)
[11] Hwang, C.L.; Masud, A.S.M., Multiple objective decision making—methods and applications, (1979), Springer Berlin
[12] J.P. Ignizio, Goal Programming and Extensions, Lexington D.C. Health, MA, 1976.
[13] Kornbluth, J.S.H.; Steuer, R.E., Multiple objective linear fractional programming, Management sci., 27, 1024-1039, (1981) · Zbl 0467.90064
[14] Kornbluth, J.S.H.; Steuer, R.E., Goal programming with linear fractional criteria, European J. oper. res., 8, 58-65, (1981) · Zbl 0486.90077
[15] Luhandjula, M.K., Fuzzy approaches for multiple objective linear fractional optimization, Fuzzy sets and systems, 13, 11-23, (1984) · Zbl 0546.90094
[16] Mohamed, R.H., The relationship between goal programming and fuzzy programming, Fuzzy sets and systems, 89, 215-222, (1997)
[17] Narasimhan, R., Goal programming in a fuzzy environment, Decision sci., 11, 325-336, (1980)
[18] Pal, B.B.; Basu, I., A goal programming method for solving fractional programming problems via dynamic programming, Optimization, 35, 145-157, (1995) · Zbl 0839.90120
[19] Romero, C., A survey of generalized goal programming, European J. oper. res., 25, 183-191, (1986) · Zbl 0586.90057
[20] Sakawa, M.; Kato, K., Interactive decision-making for multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers, Fuzzy sets and systems, 97, 19-31, (1988)
[21] Sakawa, M.; Yumine, T., Interactive fuzzy decision-making for multiobjective linear fractional programming problems, Large scale systems, 5, 105-114, (1983) · Zbl 0533.90085
[22] Steuer, R.E., An interactive multiple objective linear programming procedure, (), 225-239
[23] Tiwari, R.N.; Dharmar, S.; Rao, J.R., Fuzzy goal programming—an additive model, Fuzzy sets and systems, 24, 27-34, (1987) · Zbl 0627.90073
[24] Zadeh, L.A.; Zadeh, L.A., The concept of linguistic variable and its application to approximate reasoning, Part I, II, III, inform. sci., Part I, II, III, inform. sci., 9, 43-80, (1975) · Zbl 0404.68075
[25] Zimmermann, H.-J., Fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems, 1, 45-55, (1978) · Zbl 0364.90065
[26] Zimmermann, H.-J., Fuzzy sets, decision making and expert systems, (1987), Kluwer Academic Publishers Boston, Dordrecht
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